Geodesic
Quantum Markov Chains on Comb Graphs: Ising Model
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 192-207

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We construct quantum Markov chains (QMCs) over comb graphs. As an application of this construction, we prove the existence of a disordered phase for Ising type models (within the QMC scheme) over comb graphs. Moreover, we also establish that the associated QMC has the clustering property with respect to translations of the graph. We stress that this paper is the first one where a nontrivial example of QMCs over irregular graphs is given.
Mots-clés : quantum Markov chain, comb graph
Keywords: Ising model, clustering. 
@article{TM_2021_313_a16,
     author = {Farrukh Mukhamedov and Abdessatar Souissi and Tarek Hamdi},
     title = {Quantum {Markov} {Chains} on {Comb} {Graphs:} {Ising} {Model}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {192--207},
     publisher = {mathdoc},
     volume = {313},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_313_a16/}
}
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Farrukh Mukhamedov; Abdessatar Souissi; Tarek Hamdi. Quantum Markov Chains on Comb Graphs: Ising Model. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 192-207. http://geodesic.mathdoc.fr/item/TM_2021_313_a16/